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A surface which is simultaneously complete and minimal. There have been a large number of fundamental breakthroughs in the study of such surfaces in recent years, and they ...

The ding-dong surface is the cubic surface of revolution given by the equation x^2+y^2=(1-z)z^2 (1) (Hauser 2003) that is closely related to the kiss surface. The surface can ...

A surface that contains two families of rulings. The only three doubly ruled surfaces are the plane, hyperbolic paraboloid, and single-sheeted hyperboloid.

"Nordstrand's weird surface" is an attractive quartic surface given by the implicit equation It has 11 ordinary double points located at (2/5,0,0), (-2/5,0,0), ...

A parallel of a surface of revolution is the intersection of the surface with a plane orthogonal to the axis of revolution.

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...